Introduction – Games, whether played on a board, such as chess or Go, or played on the computer, are a major component of human culture [1]}. In the language of physics, instances of a game are trajectories, time-ordered sequences of elementary steps. The outcome of a game is a path-extensive order parameter determined by the entire history of the trajectory. Playing games was once the preserve of human beings, but machine learning methods, more specifically reinforcement learning, now outperform the most talented humans in all the aforementioned examples [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}. While there are more scientific examples of reinforcement learning [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, we choose to compare with games as they are the easiest applications to understand. Motivated by the correspondence between games and trajectories, it is natural to ask how the machine-learning and optimal control methods that have mastered game-playing might be applied to understand physical processes whose outcomes are path-extensive quantities.
